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The Perfekt is commonly used in spoken German to refer to the past.
You generally form active sentences in the Perfekt by using a conjugated form of the auxiliary verbs ‘sein’ (to be) or ‘haben’ (to have) and the past participle of the verb. Here are the conjugations of sein and haben.
sein = to be
|1st person||ich bin(I am)||wir sind(we are)|
|2nd person||du bist / Sie sind(you are)||ihr seid / Sie sind(you are)|
|3rd person||er/sie/es ist(he/she/it is)||sie sind(they are)|
haben = to have
|1st person||ich habe(I have)||wir haben(we have)|
|2nd person||du hast / Sie haben(you have)||ihr habt / Sie haben(you have)|
|3rd person||er/sie/es hat(he/she/it has)||sie haben(they have)|
You usually use haben when you do something to someone or something else and sein when something happens to you, so to speak. Please note, that it HAPPENS to you, that does not mean that someone is doing something to you, which would result in a passive sentence!
Ich habe einen Kuchen gebacken. = I baked a cake. / I have baked a cake.
Er hat einen Apfel gegessen. = He ate an apple. / He has eaten an apple.
Wir haben ein Lied gesungen. = We sang a song. / We have sung a song.
These three examples show that you did something actively, thus, you have to use the auxiliary verb ‘haben’ (to have)
Ich bin gewachsen. = I grew. / I have grown.
Er ist nach Berlin gefahren. = He went to Berlin (by car/train). / He has gone to Berlin.
Wir sind nach Deutschland geflogen. = We went to Germany (by plane).
These three examples show that something happened to you without somebody having done anything to you, thus, you have to use the auxiliary verb ‘sein’ (to be). To make my hypothesis clearer compare the following two sentences:
Er ist nach Hamburg gefahren. = He went to Hamburg.
Er hat sie nach Habburg gefahren. = He drove her to Hamburg.
You see that the Perfekt is used to expresses that an action took place in the past and is, thus, completed. The period between the action and the moment of speaking doesn’t matter.
Further, you may have discovered that the German Perfekt tense is equivalent to the English past and present perfect tense. That is, in German we don’t distinguish whether an action was completed in the past or has just been finished. Compare:
Ich habe einen Brief geschrieben. = I wrote a letter. / I have written a letter.
Ich habe Fernsehen geschaut. = I watched TV. / I have been watching TV.